Kepler's (Stellated) FractalsHop David attracted my attention to Keplerian Fractals. He replaces every horn of a stellated (nonconvex) polyhedron by small selfsimilar polyhedron. The picture shows that we can make it in two different ways (we will obtain a IItype (solid) fractal if we combine Itype ones). 
Interactive Kepler's Octahedron is made of
4 Tetra Flakes. Hop David found out that it turns into a cube under iterations.
He found "Cantor's Octahedron" beneath the cube's surface too.
Kepler's Stellated Dodecahedron Itype, IItype (solid) Kepler's Great Stellated Dodecahedron Itype, IItype (solid). Polyhedra with many vertises are too complicated :( 
Cantor's WebsYou will get 1D Fractal Web (may be Laces or Hedgehog :) if you start at "skeleton" of a Polyhedron. The skeleton is made of rays from the Polyhedron center to its verteses. Look at Interactive Tetrahedron Web and Pyramid Web. 

Koch's FlakesInteractive Tetra Flake (click it) is a simple 3D generalization of the 2D Snowflake. You take a equilateral triangle, shrink it 2 times and translate 6 copies (3 of them with rotation) to get "broken" equilateral triangle. Then repeat the process.One more 3D Koch object  Interactive Cubic Flake. 